I vote for an iMac, they're pretty nice computers. You can get a 27" refurbished for £1,199.00: http://store.apple.com/uk/product/FC813B/A
That's a 2011 model, so its fairly up to date (and you get Thunderbolt ports). Its a quad core 2.7GHz i5, which is a pretty quick processor, and the graphics card is also decent, its a 512MB HD 6770. It comes with a 7200 rpm 1TB hard drive, and 4GB 1333MHz DDR3 SDRAM, which you could upgrade up to 16GB, if you felt like you needed it for some reason. Honestly though, the best part of this computer is undoubtedly the screen. Working on a 2560x1440 27" LED screen like that is a dream. It is the brightest, sharpest, most vibrant and crystal clear display I've ever used. If you have an Apple store nearby, go and look at one of the 27" iMacs. Those things cost around 1000USD by themselves, so I feel that the iMacs are definitely the best buy once you take that into consideration.
If you spec for spec'd that computer and built it yourself, then bought a comparable display, I think you'd actually come out just about even. Its a solid computer, and a fantastic display. I have a 2 year old one, and it has no trouble with any of the multi-track recording that I do, or any of the mixing and mastering, or any of the video processing. Everything is fast and easy, I don't even have to worry about my hardware resources most of the time.